Lake bottom relief reconstruction and water volume estimation based on the subsidence rate of the post-mining area (Bytom, Southern Poland)

Mining activity leads to subsidence troughs and permanent changes in water relations, like the formation of anthropogenic reservoirs. In the Upper Silesian Coal Basin (S Poland), their number is so high that the area is called an anthropogenic lake district. Any form of water retention, in the face of climate change, is valuable. However, the problem is the high variability of these lakes, making it challenging to estimate water resources. An example of this type of anthropogenic lake is the Brandka Pond in Bytom. An original method was proposed, consisting of two stages: reconstruction of the lake bottom relief based on the initial state of the area relief in 1994, i.e. at the beginning of the reservoir formation, and the land subsidence rate calculated for this area. Archival cartographic materials and DEMs from LiDAR data were used and processed in the open-source geoinformation software. Orthophoto maps and satellite scenes were also collected to determine changes in the extent of the pond from 1993 to 2019. Bathymetric data obtained in 2019 during sonar measurements on the reservoir was used to verify the calculations. The pond began to form in the early 1990s, and by 2019, it had reached an area of 178,226 m2, a maximum depth of 5.8 m and a capacity of 421,173 m3. The reconstruction method is accurate and suitable for lakes over 2 m deep, and the calculated capacity differs from the bathymetric data by 0.2%.


Study area
The Brandka Pond is administratively located in the Silesian Voivodeship, in Bytom, on the border of the Karb, Miechowice and Stroszek districts (Fig. 1a).The study area and the reservoir are 1.75 km 2 , and the lake constitutes 10.7%.
Geologically (Fig. 1b), this area is built by a mudstone series and the Upper Silesian Upper Carboniferous sandstone series, cut by numerous faults 66 .These layers are also rich in hard coal deposits.Above the Carboniferous series are Triassic sands, sandstones, clays, claystone and mudstones, ore-bearing dolomites, limestones and marls (~ 180 m) with karst contact between Triassic and Miocene layers.The surface formations consist of Quaternary deposits (~ 20 m), mainly boulder clays and fluvioglacial sands and gravels of two glaciation episodes.Faults can also be seen in the formations below the Pleistocene layers, directly under the Brandka Pond basin.
Regarding hydrology, the northern part is located in the Vistula basin (Fig. 1c), the Szarlejka catchment, part of the Brynica and then the Przemsza catchment.In turn, the southern part of the area is located in the Oder basin, the catchment of Bytomka, belonging to the catchment of Kłodnica.The first-order water divide passes in the southern part of the research zone.
The land cover is varied (Fig. 1d).The northern part is occupied mainly by forests, and the southern part is by grassy vegetation.The buildings are located in the western part, with allotment gardens and orchards.In turn, the eastern part is dominated by the railway line and the Bytom ring road.

Data
Cartographic materials, aerial and satellite imageries, and digital elevation models (DEM) derived from the light detection and ranging technique (LiDAR) were used to determine the changes in the subsidence basin of the Brandka Pond in Bytom.The oldest acquired data are German topographic maps, called Messtischblatt (Ger.Meßtischblätter) on a scale of 1:25,000 (Supplementary Table S1).Since Germany adopted the Amsterdam Peil-AP elevation system in 1874 (changed to Normaal Amsterdam Peil-NAP in 1891; 67 ), these maps were also made in the AP/NAP elevation system 68 .For later years, topographic maps in Polish coordinate reference systems made available via WMS services were used.
The second data group was DEMs from airborne laser scanning using LiDAR: M-34-50-D-c-4-2 and M-34-50-D-d-3-1 files.These data had a spatial resolution of 1 m and an average height error of 0.15 m and are accessible in the PL-KRON86-NH (2012) and PL-EVRF2007-NH (2019) vertical systems.They were downloaded from the Polish National Geoportal 69 .
Archival orthophoto maps (Supplementary Table S2) were collected to present changes in the shoreline of the Brandka Pond.In addition, to determine the range of seasonal fluctuations of the studied reservoir, orthophoto maps were compared with selected satellite imageries (Supplementary Table S3) available on the U.S. Geological Survey (USGS) client/server interface-EarthExplorer 70 .

Data processing
This part of the work consisted of several parts: reconstruction of the former terrain relief, analysis of the height differences, pond bottom reconstruction and reconstructed model verification.The main stages and data processing steps are presented as a workflow diagram (Fig. 2).www.nature.com/scientificreports/ In the case of topographic maps in the 1965 and 1942 coordinate systems (CRSs) developed in the Kronsztad elevation system, the absolute heights were transformed to the applicable PL-EVRF2007-NH (NAP) system using the correction values published by the Head Office of Geodesy and Cartography (GUGiK) (retrieved from 78 ).DEMs were created for 1939/1941, 1958/1961, 1983 and 1993 ( 71 -Zenodo_DEM_recon.zip).
The DEM from the LiDAR data for 2012 in the PL-KRON86-NH elevation system was transformed into the PL-EVRS2007-NH elevation system; the correction value for Bytom was + 0.17 m.DEMs from 2012 and 2019 www.nature.com/scientificreports/were also resampled to a field resolution of 10 × 10 m, consistent with the values of the models reconstructed from older topographic maps.

Analysis of height differences
We calculated and presented the DEMs of Difference (DoDs) in the form of maps in 5 periods: Based on DoDs, an analysis of changes in the volume of rock masses in the studied periods was carried out using the Grid Volume tool in SAGA GIS ( 71 -Zenodo_Table2.pdf).The obtained differences were "net" values, allowing us to determine the size of the "loss" of rock masses-here: land subsidence.Then, the "net" values were divided by the surface area of the studied terrain.The average subsidence values of the entire area in meters were obtained.Dividing them by time showed the average rate of land subsidence per year.The changes were also presented as morphological profiles of the terrain using a Profile Tool plug-in for QGIS.S3).Manual delineation of the reservoir's shoreline was made based on these materials ( 71 -Zenodo_Brandka_shapes_1993-2018.zip).
We also analysed the change in the course of the first-order watershed line between the Vistula and Oder basins, using the Convergence Index for DEM from 1993 and 2019 in SAGA GIS.In this index, maximum positive values indicate ridge skeleton lines, and minimum negative values-are watercourse/valley skeleton lines.
Changes in land use were analysed based on cartographic materials published in 1889, 1943, 1958-1961, 1983  and 1993, and orthophoto maps from 2019.Manual vectorization of particular types of land use was performed.Then, the percentage share of each land use type in the study area was calculated ( 71 -Zenodo_Table4.pdf).

Land use/land cover changes in the area of Brandka Pond in the years 1881-2019
From 1881 to 2019, there were significant changes in the land cover structure in the study area (Fig. 4; 71 -Zenodo_Table4.pdf).Since the study area is located outside the centre of the Miechowice district and land subsidence was found, no significant increase in the built-up areas was observed here.However, at the expense of grassy areas, allotments and orchards appeared in 1958/1961.In 1983, a heap of post-mining waste was built in the northeastern part.Grassland decreased from 79% in 1881 to 30% in 2019.Forested areas increased from 18% in 1881 to 33% in 2019, mainly through plant succession to grassland and the heap.
One of the significant changes in land use related to human activity is the disappearance of industrial areas due to the closure of the mining shafts.In modern times, the hills of the former mine shafts of the zinc and lead ore mines (so-called warpies) can still be seen.One of the most characteristic is the "Koch" shaft, located at the northern part of the shoreline of the Brandka Pond.When water is spilt, it creates an island in the studied reservoir.

The bottom relief of the Brandka Pond
The maximum depth was 6.05 m, and this point is located in the eastern part, in the outline of the initial range of Brandka Pond in 1993 (Fig. 7a).The deepest explored place is at an altitude of 261 m a.s.l., and the coastline  S1 and S2). at 267 m a.s.l.The shallowest area is a fragment of the reservoir in the form of a bay between the former Koch shaft and a mining heap.Fragments of flooded trees in this area confirm the small depth of up to 1 m.The reconstructed depth of Brandka Pond in 2019 also allowed us to determine the subsidence value within the reservoir in the period 1939/1941-2019 (Fig. 7b).The most remarkable height differences, up to 33 m (average subsidence rate 413-423 mm per year), were observed in the western part, and the lowest, up to 22 m (average subsidence rate 275-282 mm per year), at the eastern shores of the Brandka Pond (Fig. 7c).

The Brandka Pond extent from 1993 to 2019
Changes in the spatial extent of the Brandka Pond from its formation in 1993 to 2019 were examined (Fig. 8).At that time, the Brandka Pond increased its area by 15.6 ha.The most effective rate of surface change occurred   The stabilization of the shoreline range characterizes contemporary periods.However, on the southern side of the reservoir, the adjacent floodplain in the subsidence basin-WS-47 "Bączek"-begins to develop clearly.

Verification of the reconstructed bottom relief of the Brandka Pond-the use of a bathymetric model
Comparing both DEMs, obtained by the authors based on the rate of land subsidence (Fig. 9a) and bathymetric measurements (Fig. 9b), one can notice a similar course of the reconstructed isobaths to those from the actual measurements.The similarities are particularly noticeable where the bottom is trimmed in the outline of the reservoir from 1993.One of the most visible discrepancies between the former Koch shaft and the mining heap can be found in the northern part of the Brandka Pond (Fig. 9c).Also, comparing raw data from sonar surveys with the points used to reconstruct the bottom relief confirms the highest discrepancies in this area, up to approximately 2 m (Fig. 9d).Bathymetric tests by the Silesian Water Centre showed a greater depth than the reconstructed one.In addition to areas with lower values, GIS methods also showed places with greater depths, mainly in the western and central parts of Brandka Pond.The maximum depth also turned out to be slightly greater.During the bottom reconstruction test, it was determined at 6.05 m, with bathymetric measurements at 6 m.The maximum differences between both models are − 3.84 m (shallower areas) and + 0.26 m (more deep areas), and the average is 0.23 m ± 0.88 m.The vast majority of the reservoir (70.6%) is within the depth difference range up to a maximum of ± 1 m.S2).The most significant negative discrepancy (shallower areas) between the former Koch shaft and the postmining heap and in the eastern part of the Brandka Pond (from 1 to 2 m) can be observed.In turn, the most significant positive differences (deeper areas) occur in the central part of the lake (from 1 to 3 m).
The pond volume in the case of a reconstruction attempt was 422,073 m 3 ± 370 m 3 , and according to bathymetric data, 421,173 m 3 of water.The difference amounts to 0.2% between both models.The average depth of the pond is 2.44 m from the reconstructed model and 2.4 m from the bathymetric model.

Discussion
The extraction of natural resources, especially hard coal, is an essential factor leading to the subsidence basins formation, and Bytom is one of the cities most affected by this process [12][13][14][15][16]44,51,64,81,82 . Subsidence is ccompanied by mine-induced seismicity, typical of the USCB area 23,[83][84][85][86] and the formation of fault zones.It leads to an abrupt, temporary increase in the subsidence rate, exceeding the average speed by 20-30 times.The analysis showed that the general subsidence rate is not constant but varies over time, reaching maximum values during the operation period with a shift of approximately 3-6 months 11 and then gradually slowing down.Most ground displacement occurs 1-3 years after mining stops 87 . In additon, the subsidence values are influenced by the geological structure and the mining system (especially the longwall system with caving).The more intense the rate, the more mining levels there are, and the more the analysed area is located in the centre of the subsidence basin 22 or the fault zone 27,88 .
For the area of the Brandka Pond, mining led to the removal of output together with gangue with an average thickness of 32.5 m, giving the elevation lowering of 19 m 89 and, according to our estimates, on average, 18.5 m.The maximum depression, considering the reservoir bottom, had the ordinate of 27.5 m in the eastern part of the pond and 33 m in its western part.Similar values (31 m) are quoted by 82 .In the analysed research area, the long-term subsidence rate reached the highest values in the period of the most intensive extraction, i.e. in the years 1960-1983, reaching an average of 430 mm per year, and it was about twice as high as the average calculated for the years 1943-2019.At that time, the average annual volume of hard coal extraction at USCB reached 200 × 10 6 Mg in 1980 and decreased to approximately 80 × 10 6 Mg in 2012 87 .Wagner 90 believes the area may be stable regarding residual subsidence for approximately two years after the cessation of mining.Our studies confirmed this tendency; from 2012 to 2019, it dropped to 37 mm per year.Tajduś et al. 30 present similar values in their summary for other countries.
One of the most important effects of the subsidence basin development is the constant change in water relations 13,17 .In extreme cases, an anthropogenic reservoir develops.The USCB area, in terms of lake content at the level of 2.74% 91 , occupies one of the top places in Poland, gaining the name of the Upper Silesian Anthropogenic Lake District.Many lakes are reservoirs in subsidence basins, such as Brandka Pond, created in the early 1990s.Its area has now stabilized at approximately 17 ha due to the excess water pumping out.The maximum depth reaches about 5.8 m and averages 2.4 m.The water volume is estimated at approximately www.nature.com/scientificreports/421,000 m 3 (168 Olympic swimming pools), and about 429,000 m 3 considering the pond range from 2011.However, this is a short-term situation.In 2011, the "EKOPLUS" Mining Plant was launched on the site of the liquidated coal mine "Powstańców Śląskich" 82 .This plant operates in the mining area of Bytom VII.The KWK "Bobrek-Piekary Ruch Bobrek" mine, operating in the Bytom III mining area, is also open.The resumption of hard coal mining contributes to the current land subsidence in the southern part of the research area and the expansion of the neighbouring Ws-47 lake, called Bączek.Since the Bączek Pond is developing dynamically, the Brandka Pond will probably soon capage into the Oder basin, and subsidence basins and the pond waters will merge to form a large reservoir 92 .This process is evidenced by the Brandka Pond waters pouring towards the south during the wet years (2010 and 2011).According to our estimates, the "movement" of the first-order watershed line (determined by the Convergence Index on the DEM) towards the north due to progressing subsidence south of the Brandka Pond 52,81 is up to 3.4 m per year in the eastern part, 5.1 m per year in the south-central part of the analysis area and about 0-2.5 m per year in its western part (based on data from 1958/1961-2019; cf.Fig. 7).
In the example of Bytom, one more critical problem can be noticed.In the Karb district in August 2011, a remarkably rapid subsidence occurred, the rate of which reached 245 mm within 54 days (1656 mm per year) 12 .This event led to permanent damage to buildings, bridges and installation systems, as a result of which 140 people had to leave their buildings, and about 600 people were at risk of evacuation 93 .It occurred after a period of heavy rains, which led to numerous inundations and floods in the region, and in Bytom, it also resulted in the flooding of the Brandka Pond.This example shows how dangerous subsidence basins become in urbanized areas, where additional permanent changes in water conditions occur 17 .Combining both elements puts man in a losing position, even when calculations indicate that the building's construction should withstand such intense subsidence.
Comparing the results of the pond bottom relief reconstruction with the data obtained using bathymetric measurements shows some differences in the depth of the reservoir, which may be partly due to errors and limitations of the adopted method.The degree of cartographic generalisation has evolved over the years.For this reason, the level of generalisation present on historical topographic maps, even those made on a similar scale, shows different characteristics compared to contemporary topographic maps 94 .Previous research indicates that the error in locating a given point on Prussian maps was 8-10 m, and the average height deviation was 0.5 m 95 .The errors were mainly due to the reproduction and printing of maps.For old maps at a scale of 1:25,000, with a graphic accuracy of up to 0.5 mm (the smallest distance between contour lines visible to the human eye), this means a 12.5 m terrain distance and a 1.25 m height difference (contour line interval).In our study, an uninhabited area with good contour lines was vectorised.Hence, a vertical error of 1.25 m is the maximum.Having rectified maps with a 300-400 dpi resolution, the contour line's width was approximately 5-9 rasters with sides of approximately 1 m of terrain value.It gives approximately 0.2-0.36m of vertical error.Considering the above values, it can be assumed that the vertical error of the reconstructed relief of the Brandka Pond bottom could be approximately 0.7-0.9 m.The reconstruction method is not recommended for small, shallow reservoirs.In turn, reconstructions based on DEMs from LIDAR data are burdened with a vertical error of 0.15 m.An important factor affecting the accuracy of old topographic maps is also the issue of the rectification process of the scan, during which calibration errors occur.Their average value (root-mean-square error) informs the accuracy of matching the analyzed map sheet 96 .Additional uncertainty is also caused by errors related to the quality of scanned map sheets.It depends on the scanner type and the condition in which the analyzed sheet of the old topographic map was preserved 97 .
The reconstruction accuracy may be improved by increasing the number of reference points around the lake shoreline, which contain information about the "beginning" terrain height and the subsidence rate.In our study, the points were 100 m apart (cf.Fig. 3), but smaller distances, e.g.50 or 20 m, can be used.It will increase the number of connections between the points and thus increase the number of intersections used in further calculation steps.However, the main reason for choosing the distance between reference points should be the target resolution of DEMs.
Some authors chose the Messtischblatt map published in 1889 for long-term analysis (e.g. 44,45).The subsidence rate until the 1940s was probably low, e.g. 45 estimates that between 1881 and 1962, the rate was, on average, 59 mm per year, and it increased only after a period of intensive exploitation.If we assume our calculations that in 1939/1941-1958/1961, the subsidence rate was about 220 mm per year, this means that between 1881 and 1943 it was, on average, about 17 mm per year.There is also the issue of the height difference of up to 0.17 m between vertical spatial reference systems (Amsterdam and Kronstadt) and their changes between the nineteenth and twenty-first centuries 67 included in our analysis.
One possible, probably more significant difference between the models is the failure to consider the sedimentation process 98 .According to 26 research conducted in a dried now reservoir formed in a subsidence basin, a 5-11 cm thick layer of sediments was formed during the 13-14 years of the reservoir's operation.On this basis, the average sedimentation rate was determined at the level of 3.6-8.5 mm per year.Due to the similar genesis and the nearby location of the examined reservoir, the obtained average sedimentation rate can be related to the Brandka Pond.Considering sedimentation with an average value of 5 mm per year and the development time of Pond Brandka (26 years), there should be a layer of bottom sediments with an average thickness of about 13 cm.
The obtained value can only be treated as an estimate because the development of bottom sediments depends on many factors, both on a regional and local scale 57 .According to the research on reservoirs located in the Upper Silesian-Zagłębie region, the thickness of bottom sediments ranges from 0.2 to 179.5 cm, with an average thickness of 24.3 cm 98 .One such factor is the existence of water inflows.There are no permanent watercourses in the form of rivers or streams around Brandka Pond.However, ditches draining nearby areas and roads flow into it, providing additional material as raised, suspended and dissolved 57 .Dry and wet deposition from the www.nature.com/scientificreports/atmosphere 57,99 and surface runoff 57 will be of greater importance in providing the material that builds bottom sediments.In this case, the proximity of the studied reservoir to the mining heap is not without significance.Due to precipitation and during snowmelt, objects of this type are washed away with fine material, which then falls to the lake bottom 100 .The influx of pollutants, including biogenic compounds, affects the eutrophication of the reservoir, which in turn leads to its shallowing and disappearance.According to research by 101 , the Brandka Pond was classified as a eutrophic reservoir and, according to other indicators, even as hypertrophic.The pollutants supply is also confirmed by the high water electrolytic conductivity 102 .An additional element that may affect the development of the bottom sediment layer is the vegetation currently growing on the Brandka Pond banks and flooding during the development of the studied reservoir (e.g.flooded trees in the northern part, near the former Koch shaft).As a result of flooding, the vegetation gradually dies.Then, it sinks to the lake's bottom, creating a sediment layer of organic matter 57 .It is also a reason that may cause significant differences between the reconstructed data and the data read from the sonar profile.The sonographic image is difficult to interpret, and the course of the bottom, where there is a lot of loose sediment and vegetation causing noise in reflections (see Supplementary Fig. S2), is difficult to determine.An example is the northern part of Brandka Pond, where there are submerged trees, and sonar data interpretation is challenging.

Conclusions
Our calculations have shown that the described method, based on old maps on a scale of 1:25,000, due to the possible vertical error of ± 0.7-0.9m, will be suitable for areas where reservoirs with a depth greater than 2 m have developed.The accuracy of the reconstruction can be, to some extent, regulated by the number of reference points around the modern pond shoreline, thanks to which we can increase the density of points for reconstruction and thus also influence the resolution of the resulting DEMs.
The analysis showed that in the case of eutrophic reservoirs, the problem in data verification is the low density of the bottom in the sonar image, resulting from the accumulated sediments and vegetation.Further field research is necessary here, requiring sampling of bottom sediments.They will improve the interpretation of sounding results and, therefore, the accuracy of the reconstructed models of the pond bottom relief.
The obtained results indicate that the reconstruction of the bottom relief based on the land subsidence rate, despite the limitations mentioned above, is a simple way to estimate the capacity of the pond and, thus, water resources for the needs of industry or blue-green infrastructure.At present, the water resources of the Brandka Pond account for about 0.4% of the annual water consumption for the industry in the Silesian Voivodeship in 2020 103 .Here, the most significant problem remains the previously mentioned issue of water purity.However, with certain expenditures and reclamation procedures, such reservoirs can also be recreational areas for the city, favour the local microclimate, mitigate the impact of urban heat islands, be included in the retention infrastructure and be a valuable area of increased biodiversity.In light of the analysis and due to the activation of coal mining, monitoring the subsidence rate of the Brandka Pond and the neighbouring Bączek Pond is necessary.Everything indicates that both lakes will soon merge, and further pumping out excess water will not be profitable.The development of this area towards including it in the blue-green infrastructure for Bytom should be a priority for the city's decision-making institutions.

Figure 7 .
Figure 7.The relief of the Brandka Pond bottom and its surroundings in 2019: (a) the reconstructed depth of the Brandka Pond in 2019; (b) calculated subsidence values within the Brandka Pond from 1939/1941-2019; (c) latitudinal morphological profiles by the study area, taking into account the bottom of the Brandka Pond for selected years from 1939/1941-2019; vertical exaggeration × 22 (based on topographic maps-see Supplementary Table S1 and DEMs from LiDAR data from 2012 and 2019 69 , the lake shoreline based on the orthophoto map from 2019).Legend explanation (parts a and b): 1-maximum and minimum elevation, 2deepest point/maximum of the bottom subsidence, 3-lowest point of the Brandka bottom, 4-profile line, 5-1st order watr divide line in 1958/1961, 6-1st order water divide line in 2019, 7-contour line interval 5 m, 8-Brandka Pond in 1993, 9-Brandka Pond in 2019.Image generated with QGIS 3.34.0Prizren 72 .
Figure 7.The relief of the Brandka Pond bottom and its surroundings in 2019: (a) the reconstructed depth of the Brandka Pond in 2019; (b) calculated subsidence values within the Brandka Pond from 1939/1941-2019; (c) latitudinal morphological profiles by the study area, taking into account the bottom of the Brandka Pond for selected years from 1939/1941-2019; vertical exaggeration × 22 (based on topographic maps-see Supplementary Table S1 and DEMs from LiDAR data from 2012 and 2019 69 , the lake shoreline based on the orthophoto map from 2019).Legend explanation (parts a and b): 1-maximum and minimum elevation, 2deepest point/maximum of the bottom subsidence, 3-lowest point of the Brandka bottom, 4-profile line, 5-1st order watr divide line in 1958/1961, 6-1st order water divide line in 2019, 7-contour line interval 5 m, 8-Brandka Pond in 1993, 9-Brandka Pond in 2019.Image generated with QGIS 3.34.0Prizren 72 .
Figure 7.The relief of the Brandka Pond bottom and its surroundings in 2019: (a) the reconstructed depth of the Brandka Pond in 2019; (b) calculated subsidence values within the Brandka Pond from 1939/1941-2019; (c) latitudinal morphological profiles by the study area, taking into account the bottom of the Brandka Pond for selected years from 1939/1941-2019; vertical exaggeration × 22 (based on topographic maps-see Supplementary Table S1 and DEMs from LiDAR data from 2012 and 2019 69 , the lake shoreline based on the orthophoto map from 2019).Legend explanation (parts a and b): 1-maximum and minimum elevation, 2deepest point/maximum of the bottom subsidence, 3-lowest point of the Brandka bottom, 4-profile line, 5-1st order watr divide line in 1958/1961, 6-1st order water divide line in 2019, 7-contour line interval 5 m, 8-Brandka Pond in 1993, 9-Brandka Pond in 2019.Image generated with QGIS 3.34.0Prizren 72 .